Solve the system of equations given by 5x - 2y = -6 and 15x - 6y = 6

A. Infinitely many solutions
B. (1, 1)
C. No solution
D. ( -2, -2)

Step-by-step explanation:

cost of adult ticket, AT = $22

Cost of child ticket, CT = $15

Difference in price, D = AT-CT = 22-15 =$7

Difference in price for 3 tickets = 3D = $21

Answer:

Three Adult Tickets will be $22 more than Three Children's Ticket

Step-by-step explanation:

One Adult= $22

One Child =$15

Three adults= $22 x 3= $66

Three Children= $15 x 3= $45

$66 - $45= $21

Answer:

Johnny

Step-by-step explanation:

I don't think you put the whole question out

[tex]\bf ~~~~~~ \textit{Simple Interest Earned} \\\\ I = Prt\qquad \begin{cases} I=\textit{interest earned}\dotfill&2,625\\ P=\textit{original amount deposited}\dotfill & \$25,000\\ r=rate\to 3.5\%\to \frac{3.5}{100}\dotfill &0.035\\ t=years \end{cases} \\\\\\ 2625=(25000)(0.035)t\implies \cfrac{2625}{(25000)(0.035)}=t\implies 3=t[/tex]

Answer:

The  number of years = 3 years

Step-by-step explanation:

Points to remember

Simple interest

I = PNR/100

Where P - Principle amount

N - Number of years

R - Rate of interest

To find the number of years

Here P = 25,000

R = 3.5% and I = 2625

I = PNR/100

N = (I * 100)/PR

 = (2625 * 100)/(25000 * 3.5)

 = 3 years

Therefore number of years = 3 years

Answer:

B: 12.2cm

Step-by-step explanation:

Got it right on edge 2021✅

I doubt it says "or". It's probably an and.

[tex]\dfrac{-2}{3}x > 8\wedge\dfrac{-2}{3x} < 4[/tex]

[tex]-2x > 24\wedge3x < \dfrac{4}{-2}[/tex]

[tex]x > -12\wedge x < -\dfrac{2}{3}[/tex]

[tex]\Rightarrow\boxed{-12 < x < -\dfrac{2}{3}}[/tex]

[tex]\Rightarrow\boxed{x\in(-12,-\dfrac{2}{3})}

[/tex]

Hope this helps.

r3t40

Answer:

{x | x < -12 or x > -6}

Answer:

49

Step-by-step explanation:

I think I have read this right!

You let me know if you did not mean to write the following:

[tex]\sum_{k=1}^{7}(1+(k-1)(2)[/tex]

Alright so the lower limit is 1 and the upper limit is 7.

All this means is we are going to use the expression 1+(k-1)(2) and evaluate it for each natural number between k=1 and k=7 and at both k=1 and k=7.

The sigma thing means we add those results.

So let's start.

Evaluating the expression at k=1: 1+(1-1)(2)=1+(0)(2)=1+0=1.

Evaluating the expression at k=2: 1+(2-1)(2)=1+(1)(2)=1+2=3.

Evaluating the expression at k=3: 1+(3-1)(2)=1+(2)(2)=1+4=5.

Evaluating the expression at k=4: 1+(4-1)(2)=1+(3)(2)=1+6=7.

Evaluating the expression at k=5: 1+(5-1)(2)=1+(4)(2)=1+8=9.

Evaluating the expression at k=6: 1+(6-1)(2)=1+(5)(2)=1+10=11.

Evaluating the expression at k=7: 1+(7-1)(2)=1+(6)(2)=1+12=13.

Now for the adding!

1+3+5+7+9+11+13

  4+  12+    20+13

        16+     33

           49

Answer:

Option C is correct.

Step-by-step explanation:

We are given

1452 divided by 44 = (1452 divided by 4) divided by 11

We know that 44 = 4*11

So, 4 and 11 are factors of 44.

This division problem uses the method of Factors.

Option C is correct.

Answer:

[tex]\large\boxed{x^\frac{5}{3}y^\frac{1}{3}}[/tex]

Step-by-step explanation:

[tex]\text{Use}\ \sqrt[n]{a^m}=a^\frac{m}{n}\ \text{and}\ \sqrt[n]{ab}=\sqrt[n]{a}\cdot\sqrt[n]{b}\\\\\\\sqrt[3]{x^5y}=\sqrt[3]{x^5}\cdot\sqrt[3]{y^1}=x^\frac{5}{3}y^\frac{1}{3}[/tex]

Answer:

B

Step-by-step explanation:

edge 2021

Answer:

{x,y} = {3,1}

Step-by-step explanation:

// Solve equation [1] for the variable  x  

 [1]    x = -2y + 5

// Plug this in for variable  x  in equation [2]

  [2]    3•(-2y+5) + 5y = 14

  [2]     - y = -1

// Solve equation [2] for the variable  y  

  [2]    y = 1

// By now we know this much :

   x = -2y+5

   y = 1

// Use the  y  value to solve for  x  

   x = -2(1)+5 = 3

Solution :

{x,y} = {3,1}

For this case we have the following system of equations:

[tex]x + 2y = 5\\3x + 5y = 14[/tex]

To solve, we multiply the first equation by -3:

[tex]-3x-6y = -15[/tex]

We add the equations:

[tex]-3x + 3x-6y + 5y = 14-15\\-y = -1\\y = 1[/tex]

We look for the value of the variable "x":

[tex]x + 2 (1) = 5\\x + 2 = 5\\x = 5-2\\x = 3[/tex]

Thus, the solution of the system is (3,1)

Answer:

(3,1)

AB= 20 and AB is the full line.

We will have to divide the length of the segment by 2 to find AC.

20/2= 10

AC is 10 units. Hope this helps!

Answer: the answer is: AC= 10

Step-by-step explanation:

you can imagine a line that represents AB with 20cm of large and the midline is located in the middle of this line; this means that AC is the half of AB

So in number=

[tex]AC= AB/2[/tex]

replacin [tex]AB[/tex]

[tex]AC= 20/2[/tex]

[tex]AC=10[/tex]

1. 12 mph, 24 miles

2. m=4, y=22

3.15/1, $1500

4. x=30 y=60, k cheaper, j cheaper

Answer:

8

Step-by-step explanation:

To find Y, find X first. Multiply 2 by W (3) which is 6, and divide by 3, which gives us X=2. The inequality W+Z=X+Y substituted is 10=2+Y. Subtract 2 from 10 and you get Y=8

Answer:

13) 8

14) 2X  or 4W/3 (depending on what the choices are)

Step-by-step explanation:

So I'm using the box given:

If                                 then

W  X                            W+Z=X+Y and 2W=3X

Y    Z

13)

3   X                           3+7=X+Y and 2*3=3*X

Y   7

To get W,X,Y, and Z I compared it to the first lay out and then replace the other W's,X's,Y's, and Z's.

So we have 3+7=X+Y which means 10=X+Y.

We also have 2*3=3*X which means 2=X (I divided both sides by 3).

If X=2 then 10=X+Y gives us 10=2+Y.

10=2+Y can be solved by subtracting 2 on both sides:

8=Y

Y=8

14)

W  X                                  W+W=X+Y and 2W=3X

Y   W

So W+W=X+Y means 2W=X+Y

We are also given 2W=3X which means by substitution into the first equation we get 3X=X+Y.

3X=X+Y can be solved by subtracting X on both sides:

2X=Y

We can also write Y in terms of W.

We have 2W=3X so that means X=2W/3 (I divided both sides by 3)

Now I'm going to replace X in 2X=Y with (2W/3) giving me:

2(2W/3)=Y

4W/3=Y

Answer:

The graph in the attached figure

Step-by-step explanation:

we know that

The equation of the line into slope intercept form is equal to

[tex]y=mx+b[/tex]

where

m is the slope

b is the y-intercept

In this problem we have

[tex]m=-\frac{1}{3}[/tex]

[tex]b=-3[/tex]

substitute

[tex]y=-\frac{1}{3}x-3[/tex]

To graph the line find out the intercepts

Find the y-intercept

The y-intercept is the value of y when the value of x is equal to zero

so

For x=0

[tex]y=-\frac{1}{3}(0)-3=-3[/tex]

The y-intercept is the point (0,-3) -----> is a given value

Find the x-intercept

The x-intercept is the value of x when the value of y is equal to zero

so

For y=0

[tex]0=-\frac{1}{3}x-3[/tex]

[tex]x=-9[/tex]

The x-intercept is the point (-9,0)

Plot the intercepts and join the points to graph the line

see the attached figure

To graph the line with a slope of -1/3 and a y-intercept of -3, plot the y-intercept at (0, -3) and use the slope to find additional points. Connect the points to graph the line.

To graph the line with a slope of -1/3 and a y-intercept of -3, we can start by plotting the y-intercept at the point (0, -3). Then, using the slope, we can find additional points on the line. Given that the slope is -1/3, we can move down 1 unit and to the right 3 units from the y-intercept to find the next point. We can continue this process to find more points and then connect them to graph the line.

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Answer:

7/5

Step-by-step explanation:

Slope intercept form is y=mx+b. It is called that because it tells us the slope,m, and the y-intercept, b.

So we can solve your given equation to find m the slope.

7x-5y=10

Subtract 7x on both sides:

-5y=-7x+10

Divide both sides by -5

y=(-7/-5)x+(10/-5)

Simplify:

y=(7/5)x+-2

m=7/5 so 7/5 is the slope.

Answer:

8

15

Step-by-step explanation:

To find the GCF of numbers, first find the prime factorizations of the numbers. The GCF is the product of common factors with lowest exponent.

GCF (16, 24)

16 = 2^4

24 = 2^3 * 3

GCF = 2^3 = 8

GCF (15, 45, 60)

15 = 3 * 5

45 = 3^3 * 5

60 = 2^2 * 3 * 5

GCF = 3 * 5 = 15

Answer:

A=8, B= 15

Step-by-step explanation:

Answer:

See below.

Step-by-step explanation:

You didn't need to.

The angle adjacent to angle x = 45 degrees (alternate interior  angle to the angle marked 45).

So x = 180 - 45 = 135 degrees.

Answer:

C. 135

Step-by-step explanation:

In the figure above, line M is parallel to line N. The value of x is 135.

x = 180 - 45 = 135

Answer:

The total length of the molding is 21 feet and 6 inches

Step-by-step explanation:

* Lets explain how to solve the problem

- The length of the two pieces are 8 feet 7 inches and 12 feet 11 inches

- Each foot has 12 inches

- Lets change the lengths of the two pieces to inch

# First piece 8 feet 7 inches

∵ 1 foot = 12 inches

∴ 8 feet 7 inches = 8 × 12 + 7

∴ 8 feet 7 inches = 96 + 7

∴ 8 feet 7 inches = 103 inches

# Second piece 12 feet 11 inches

∵ 1 foot = 12 inches

∴ 8 feet 7 inches = 12 × 12 + 11

∴ 8 feet 7 inches = 144 + 11

∴ 8 feet 7 inches = 155 inches

- To find the total length add the two answers

∴ The total length of the molding = 103 + 155 = 258 inches

- Divide the answer by 12 to change it to feet

∵ 258 ÷ 12 = 21.5 feet

- To change it to feet and inch multiply 0.5 feet by 12

∵ 0.5 × 12 = 6 inches

∴ The total length of the molding is 21 feet and 6 inches

[tex]4(4a+6b) =16a+24b[/tex]

Answer:

True

Step-by-step explanation:

Take 4/11 and you get 0.363636363636, which is the same if you take 12/33.  So the proportion of the two is the same.

Answer:

True

Step-by-step explanation:

To find out if the proportion is true you have to find out what multiplied by 4 equals 12.

To find that out you have to divide 12 by 4 which equals 3.

Now you have to do the same for the denominators. So, 33/11 equals 3.

The proportion is true because the numerator and denominator are both multiplied by 3 to get 12 to 33.

Hello! What is this for?

Also, The answer is: The lead pattern would be in the shape of a circle.

Answer: The Circle!

Step-by-step explanation:

just took the test!

Answer:

√3 - 2.

Step-by-step explanation:

Let A = 330 degrees so  A/2 = 165 degrees.

tan A/2 = (1 - cos A) /  sin A

tan 165 = (1 - cos 330) / sin 330

= (1 - √3/2) / (-1/2)

=  -2(1 - √3/2)

= -2 + 2 * √3/2

=  √3 - 2.

Answer:

[tex]\sqrt{3}[/tex] - 2

Step-by-step explanation:

Using the half- angle identity

tan( [tex]\frac{x}{2}[/tex] ) = [tex]\frac{sinx}{1+cosx}[/tex]

[tex]\frac{x}{2}[/tex] = 165° ⇒ x = 330°

sin330° = - sin30° = - [tex]\frac{1}{2}[/tex]

cos330° = cos30° = [tex]\frac{\sqrt{3} }{2}[/tex]

tan165° = [tex]\frac{sin330}{1+cos330}[/tex]

            = [tex]\frac{-\frac{1}{2} }{1+\frac{\sqrt{3} }{2} }[/tex]

            = - [tex]\frac{1}{2}[/tex] × [tex]\frac{2}{2+\sqrt{3} }[/tex]

            = - [tex]\frac{1}{2+\sqrt{3} }[/tex]

Rationalise by multiplying numerator/ denominator by the conjugate of the denominator

The conjugate of 2 + [tex]\sqrt{3}[/tex] is 2 - [tex]\sqrt{3}[/tex], hence

tan 165°

= - [tex]\frac{2-\sqrt{3} }{(2+\sqrt{3})(2-\sqrt{3})  }[/tex]

= - [tex]\frac{2-\sqrt{3} }{4-3}[/tex]

= - (2 - [tex]\sqrt{3}[/tex] )

= - 2 + [tex]\sqrt{3}[/tex] = [tex]\sqrt{3}[/tex] - 2

Answer:

C

Step-by-step explanation:

Substitute t = - 3 into h(t), then substitute value obtained into g(t)

h(- 3) = (- 3)² - 2 = 9 - 2 = 7, then

g(7) = (2 × 7) + 2 = 14 + 2 = 16 → C

Answer:

I just got done doing this. Full answers to all 4 problems are down below. All correct answers are bolded.  

Step-by-step explanation:

First problem: x2 + -8 x = 9

Add 16 to each side x2 – 8x = 9 to complete the square.

Now that you have x² - 8x + 16 = 9 + 16, apply the square root property to the equation. Answer: (x – 4)² = 25

Choose the solutions to the quadratic equation x2 – 8x – 9 = 0. Answer: -1, 9  

The equation x² - 8x - 9 = 0 can be written as x² +(-8x) = 9 which is of the form  x² + bx = c  where,

b = -8

c = 9

An equation is a mathematical statement which equate two algebraic expressions. An equation has an equal to (=) sign in between the expression.

The given equation is

x² - 8x - 9 = 0.

⇒ x² - 8x = 9

⇒ x² +(-8x) = 9

So the given equation is written of the form x² + bx = c, where,

b = -8

c = 9

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Answer:

-7 +c

Step-by-step explanation:

(7-c)(-1)

Distribute the -1

-1*7 -1*(-c)

-7 +c

Answer: Y = -3x-2

Step-by-step explanation:

if there are two co-ordinates (x1,y1) and (x2,y2).

If the line is passing through these co-ordinates

Then Slopw of the line  = (y2-y1)/(x2-x1)

We have one co-ordinate (-0,-2) let it be (X1,Y1)

Let second co-ordinate be (X,Y)

Slope = -3 = (Y-(-2)) / (X-0)

-7  = (Y+2)/(X)

Y+2 = -3 (X)

Y+2 = -3X

ADDING -2 ON BOTH SIDES OF THE EQUATION

Y+2-2 = -3X-2

Y = -3x-2

Answer:

If you choose any value for k other than 6, that will be give you the one solution.

If k=6, you have no solutions because the lines will be parallel.

Step-by-step explanation:

We are going to put each of this in y=mx+b where m is the slope and b is the y-intercept.

kx+2y=5

Subtract kx on both sides:

    2y=-kx+5

Divide both sides by 2:

     y=(-k/2)x+(5/2)

The slope is -k/2 and the y-intercept is 5/2

3x+y=1

Subtract 3x on both sides:

     y=-3x+1

The slope is -3 and the y-intercept is 1.

We want the system to have one solution so we want the slopes to be difference.

So we don't want (-k/2)=(-3).

Multiply both sides by -2: k=6.

We won't want k to be 6.

Answer:

yes

Step-by-step explanation:

7 * 6 = 42

Answer:

Step-by-step explanation:

Firstly you must understand you want to get the value of  y.

So put in values into equation which make x.

To understand here lets look at  y = 0

if y is to be 0 then x is 3.

If we substitute this value into equation (B) we get the result.

Now we have identified our answer, all is left is to substitute all other values of x and see if y are true.

So , we can see B is the answer

Answer: B

Step-by-step explanation:

The answer has to be either A, or B, because when x input is negative, the y input is positive. Visa versa.

Then just input x and y into the equation to see which answer is correct.

First let’s do A: 12=-2(-3)-6

12=6-6

12 doesn’t equal 0, so A is incorrect

So then B is the obvious solution, but let’s solve it to make sure: 12=-2(-3)+6

12=6+6

This equation is true, so the answer is B

Answer:

[tex]\large\boxed{A.\ \left\{\begin{array}{ccc}-3x+y=12\\-2x+4y=18\end{array}\right}[/tex]

Step-by-step explanation:

[tex]\underline{+\left\{\begin{array}{ccc}-3x+y=12\\x+3y=6\end{array}\right}\qquad\text{add both sides of the equations}\\.\qquad-2x+4y=18\\\\\text{therefore}\\\\\left\{\begin{array}{ccc}-3x+y=12\\-2x+4y=18\end{array}\right[/tex]

Using the equation of the sum of the system of equations and the first equation of the system, the equivalent system of equations is:

-3x + y = 12

-2x + 4y = 18

(Option A)

Given the system of equations:

Add Eqn. 1 and Eqn. 2 together:

-3x + y = 12

x + 3y = 6 (ADD)

-2x + 4y = 18

Therefore, using the equation of the sum of the system of equations and the first equation of the system, the equivalent system of equations is:

-3x + y = 12

-2x + 4y = 18

(Option A)

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Answer:

c=13.2 units

Step-by-step explanation:

step 1

Find the measure of angle C

Remember that the sum of the internal angles of a triangle must be equal to 180 degrees

so

A+B+C=180°

substitute the given values

16°+49°+C=180°

65°+C=180°

C=180°-65°=115°

step 2

Find the measure of c

Applying the law of sines

c/sin(C)=a/sin(A)

substitute the given values and solve for c

c/sin(115°)=4/sin(16°)

c=4(sin(115°))/sin(16°)

c=13.2 units